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Abstract
In this study, magneto-refractive effects of PbS quantum dots (QDs)-doped liquid core fiber with different particle sizes were investigated. Based on the density function theory, the defect structures of PbS nanoclusters were constructed and the spin magnetic moments of sulfur (S) and plumbum (Pb) were analyzed. It indicates that the magnetic moments are mainly induced by the spin interaction between Pb 6s, 6p, and S 3p states, and the spin magnetism shows a weakening trend as the particle size increases. Based on the analysis, we experimentally studied the magneto-refractive effect with different sizes PbS QDs in liquid core fibers through a magneto-refractive index measuring system. The experimental results show that the magneto-refractive effect is strong as the size of PbS QDs decreases when the concentration is 8 mg/mL, exhibiting a maximum magneto-refractive sensitivity of -1.668×10−3 RIU/mT under the magnetic field of 0-7.89 mT, which can be used for magnetic field sensing applications.
© 2022 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Magneto-refractive effect (MRE), defined as a change in refractive index of a material due to a change in the conductivity when surrounding in a magnetic field. It is a linear magneto-optical effect that occurs in liquids composed mainly of chiral molecules [1]. Specially, the magneto-refractive effect relies on the non-diagonal component of the effective dielectric tensor, which is difference with the traditional magneto-optical effect [2]. Many literatures have been focused on magneto-refractive materials, including metallic thin films [3,4], mixed-metal multilayers [5], magnetic fluids [6,7], rare earth doped optical fibers [8,9], quantum dot materials, etc., which shows great potential in the areas such as nonlinear optics [2], giant magnetoresistive (GMR) detection [10–12], and magnetic field sensing [13–15], etc.
It is well known that quantum dots exhibit many optical and physical properties different from those of macroscopic bulk materials due to their quantum effects, such as size effect, surface effect, quantum confinement effect and quantum tunneling effect. Quantum dots also exhibit unique magnetic properties under the action of magnetic field. Under the magnetic field, the quantum effect and spin effect in multi-electron planar quantum dots will be coupled [16], and this spin interaction will lead to the alternating crossover of spintronic energy levels in the energy spectrum, namely Zeeman splitting [17]. With the increase of magnetic field, the magnetic susceptibility of quantum dots will also change from paramagnetism to diamagnetism [18]. Moreover, the electron spin changes direction in interaction with lattice oscillations, impurity atoms and defects, and collisions with surfaces [19]. The spintronic transitions and energy changes of the system will further destroy the symmetry of the system. Therefore, the physical properties of quantum dots such as impurity state, symmetry, wave function, magnetic moment, susceptibility and even refractive index are all affected by magnetic field [20–22]. Unlike transition metals and rare earth metal materials, PbS QDs as a narrow-gap semiconductor, have advantage of not easily oxidized, spectrally stable, thermally stable [23], strong nonlinear effects [24]. PbS materials are not inherently magnetic. However, under an external magnetic field, it shows different magnetic properties as the structure of PbS QDs is no longer symmetric, and unpaired spinning electrons are introduced. The refractive index of PbS QDs is closely related to the magnetization, thus effective modulation of its refractive index can be further achieved by controlling the spin magnetization and coupling parameters of the quantum dots by modulating the external magnetic field. In addition, due to size effect, quantum dot size has great difference in magneto-refractive effect performance [25–27], but device performance is highly dependent on the characteristics of quantum dots and device structure. Therefore, it is very important and necessary to quantitatively understand the effects of size parameters and magnetic field on magneto-refractive properties, which will also affect the application prospects of quantum dot fiber sensors in magnetic sensor components and other optical sensors.
In this work, magneto-refractive effects of PbS QDs-doped liquid core fiber with different particle sizes were studied. We established defect structures of PbS nanoclusters with different particle sizes based on density function theory theoretically, calculated the spin parameters related to the magneto-refractive effect under spin coupling. To verify the magneto-refractive performance of PbS QDs, we investigated experimentally in liquid-core fibers with different concentrations and particle sizes. This research opens a way to broaden the quantum magnetic field sensing applications based on PbS QDs.
2. Theoretical analysis and simulation
2.1 Theoretical analysis
If a magnetic field is applied, the Hamiltonian of QDs can be written as [16]:
The above equation can solve the energy according to the Schrodinger equation and the given wave function. To simplify the calculation, the magnetization and susceptibility of the system in the state $(n,\ell ,s)$ can be expressed as:
2.2 Theoretical simulation
Since the spin-orbit interaction plays a dominant role and influences the magnetic properties of the quantum dots system, the magnetic susceptibility of the system is closely related to the spin magnetic moment and quantum dot size, which are important factors for investigation. Here, we theoretically study the spin magnetic moment characteristics of PbS nanoclusters with different sizes and the relationship between them. Due to the surface traps are ubiquitous to nanoscopic semiconductor materials [29]. The PbS QDs with {110} and {111} surfaces exposed will introduce the trap energy levels in the bandgap, and the Pb atoms on the {111} and {110} surfaces are the main sources of trap states [30]. Therefore, we simulate the spintronics situation in the defect state by Guassian 09W software and the Multiwfn program [31]. Based on the first-principles density functional method, the atomic interaction, spintronic structure, and magnetic properties of PbS nanoclusters are studied, which is helpful to further explain the magneto-refractive mechanism of quantum dots.
We established micro-defect models of PbS nanoclusters with three different sizes as shown in Fig. 1. The structures were optimized by the density functional B3LYP method. The S element was calculated using 6-31G ** and the Pb element was calculated using the Lan2ldz base group [32]. Figure 1 shows the microstructure model of defects in PbS nanoclusters and the spin electron density. When the Pb atomic defect exists in the cluster structure, the structure changes from symmetry to asymmetry, and the ground spin state of the defect cluster structure is a triplet. The bond length of Pb-S is about 2.695 to 2.882 Å. The molecular three-dimensional dimensions of Fig. 1(a-c) were calculated [33], and were 13.536 Å×10.812 Å×10.325 Å, 16.683 Å×16.071 Å×9.985 Å, 19.427 Å×17.826 Å×17.151 Å, respectively, indicating that the molecular model reached the nanometer level.
Fig. 1. Microstructure model of defects in PbS nanoclusters (a) Pb17S18, (b) Pb23S24, (c) Pb31S32 (Cyan is Pb atom, yellow is S atom, red is spin-up electron density, blue is spin-down electron density).
It can be seen from Fig. 1, that the spin electron density is mainly concentrated on S near the Pb-defect position. In Fig. 1(a), the spin magnetic moment of the Pb17S18 structure is 2 µB, in which S contributes nearly 95.8%, up to 1.916 µB. In Fig. 1(b), the spin magnetic moment of the Pb23S24 structure is approximately 1.99997 µB; In Fig. 1(c), the spin magnetic moment of the Pb31S32 structure is 1.99996 µB. When there is no defect in the PbS cluster, the ground state is a singlet and there is no magnetic moment, so the magnetic moment is mainly caused by the defect asymmetric structure [30]. When a Pb is missing, the S atom bonded to it lacks the paired electrons, and the spinning electrons are concentrated near the defect atom.
The HOMO-LUMO gap is a fundamental parameter for the design of organic electronic devices such as electroluminescent displays, image sensors, and photocells [34]. In addition, the difference in HOMO-LUMO energy between the highest occupied orbital and the lowest unoccupied orbital can be used to measure whether a molecule is easily excited and conductive: the smaller the bandgap, the more easily excited and conductive the molecule is. The smaller HOMO-LUMO gap is due to better electron delocalization [35]. As shown in Table 1, we found that HOMO-LUMO energy levels gap for spin up is larger than spin down in these three models, the HOMO-LUMO gap between spin up and spin down gradually decreases as the number of atoms decreases, as does the difference between spin up and spin down band gap. It indicates that the smaller the size is, the easier the molecule is to be excited, resulting in spin coupling interaction and better conductivity. Among the three structures, S in the Pb31S32 cluster structure provides the largest spin magnetic moment, but the spin magnetic moment direction of Pb is opposite, resulting in a total spin magnetic moment smaller than Pb17S18.
Table 1. HOMO-LUMO gap and spin magnetic moment of defects model in PbS nanoclusters
To explore the origin of defect structure magnetism in PbS nanoclusters, we further analyze the spin population of atomic orbitals. In the case of Pb17S18 cluster structure, it is found that the spin magnetic moment is mainly provided by Pb 6s, 6p, and S 3s, 3p states. The contribution ratios of S 3p, Pb 6s, Pb 6p and S 3s states to spin population are 81%, 9%, 6%, and 3%, respectively. Therefore, net asymmetry of electron density in PbS defect structure is mainly due to the spin coupling of Pb 6p, Pb 6s, and S 3p state, resulting in the spin magnetic moment, which is also the main source of defect structure magnetism in PbS nanoclusters. Moreover, as the number of atoms decreases and the size of quantum dots decreases, the magnetic moment of spin increases, the HOMO-LUMO band gap decreases, and the magnetic and electrical conductivity becomes stronger. The magneto-refractive effect will be more significant, which is consistent with the theoretical analysis results.
3. Experimental setup
3.1 Experimental characterization
In the experiments, the oil-soluble PbS QDs were provided by Suzhou Xingshuo Nanotech Co., LTD. The morphology, size, and particle size distribution of PbS QDs were observed by a field emission electron microscope (JEM-2010F, JEOL, Japan). The fluorescence emission spectrum and UV-visible near-infrared diffuse reflectance absorption spectrum were measured by a full-functional fluorescence spectrometer (FLS920, Edinburgh Instruments, UK) and UV-visible near-infrared spectrophotometer (UV3600IPLUS, Shimadzu, Japan), respectively. As shown in Fig. 2(a-h), TEM observation and particle size statistics show that the average size of the four PbS QDs is about 4 nm, 5.25 nm, 5.75 nm, and 6.5 nm, respectively.
Fig. 2. TEM images and particle size distribution of PbS QDs (a) and (e) 4 nm, (b) and (f) 5.25 nm, (c) and (g) 5.75 nm, (d) and (h) 6.5 nm.
Its absorption spectrum and fluorescence emission spectrum are shown in Fig. 3. The wavelength of 4 nm-6.5 nm PbS QD’s emission peak is located at 1034 nm, 1307 nm, 1370 nm, and 1527 nm, respectively. The first absorption peaks are located at 950 nm, 1250 nm, 1352 nm, and 1492 nm, respectively. The positions of absorption and fluorescence peaks are redshifted with the increase of particle size. According to the position of absorption peak, the particle size of PbS QDs can be roughly estimated, and the equation is as follows [36]:
where ${E_\textrm{g}}$ represents the energy level of the first absorption peak, represented by electron volt (eV); d is the diameter of the quantum dots, expressed in nanometer; $\lambda$ is the wavelength of the position of the first absorption peak; h is Planck's constant, $h = 4.0136 \times {10^{ - 15}}eV \cdot s$; c is the speed of light, $c = 3 \times {10^8}m/s$. The sizes of PbS QDs corresponding to absorption peaks estimated by Eq. (7) are 4.08 nm, 5.32 nm, 5.78 nm, and 6.45 nm, respectively, which have a small difference with the test results and relatively uniform particle size distribution.3.2 Experimental system
To study the magneto-refractive properties of PbS QDs, a magneto-refractive measuring system setup was built, as shown in Fig. 4. It mainly includes a laser as the light source, beam splitter, mirror, attenuator, cuvette for placing the PbS QDs-doped liquid core fiber, the objective lens for amplifying the optical signal, CCD for recording the interference imaging, an electromagnet for generating the magnetic field, and an HT108 tesla meter for monitor the magnetic field. The system is composed of a transmission interference optical system based on Mach-Zehnder. The laser emits light at a wavelength of 532 nm, which is then divided into two beams by a beam splitter after passing through an attenuator. A beam of light passes through the optical fiber and is amplified by the objective to collect magnetization information, which forms an interference signal with another beam of reference light on the beam splitter and is captured by a CCD image sensor.
Firstly, an appropriate amount of PbS quantum dot powder 4 mg was weighed by a high-precision electronic balance, and placed in a washed and dried test tube; Take 0.5 ml of n-hexane solution with a micropipette; The test tube containing the solution is placed into an ultrasonic oscillator and oscillated to uniformly disperse the quantum dots in n-hexane. Then the quantum dot solution is filled into the hollow core fiber (inner diameter d = 50 µm; outer diameter D = 145 µm; length L= 5-8 cm). A fiber containing PbS quantum dots with n-hexane as fiber core background were prepared. Both ends of the fiber are encapsulated with a UV glue and cured by a UV lamp for 10 min. Finally, the prepared PbS quantum dot liquid core fiber was placed in a cuvette with matching liquid, and the optical path was kept perpendicular to the optical fiber and magnetic field. The preparation of quantum dots liquid-core optical fiber the microscopic image of the sample and holographic images as shown in Fig. 5(a) and (b), respectively. The two-dimensional and one-dimensional phase diagrams of the measured experimental system are showed in Fig. 5(c) and (d), respectively. The data is recorded in the form of a computer digital hologram to achieve the reproduction and analysis of the refractive index distribution of the fiber.
Fig. 5. Preparation of PbS QDs-doped liquid core fiber (a) Microscope image, (b) Digital holograms, (c) Two-dimensional phase diagram, (d) One-dimensional phase diagram.
The phase distribution extracted by an digital holographic microscopy is the result of integrating the sample refractive index with the sample thickness [37,38]:
by substituting the fiber phase distribution into the refractive index calculation formula, the refractive index distribution of the fiber to be measured can be obtained:As we all know, the refractive index of a solution is a function of its temperature, concentration, wavelength of the incident light, and magnetic field, which can be described as $n\textrm{ }({T,\textrm{ }c,\textrm{ }\lambda ,\textrm{ }B} )$. The change of refractive index is:
In the experiment, the temperature influence was ignored as the experiment was performed at room temperature. At a given propagation wavelength, the refractive index tunability of quantum dots can be realized by changing the intensity of the magnetic field and the concentration of the solution, which has great application potential in magnetic field sensing.
3. Results analysis
First, the relationship between the concentration of PbS QDs and the magnetic field was studied. The QD surface is a highly dynamic region, coordinated by chemical species (ligands) and exposed to the surroundings (solvents and other species in solution, matrices, etc.) that can have drastic effects on the QD properties [29]. The evaporation rate, viscosity and dispersion of the solvent affect the aggregation and compactness of QDs solution [39]. N-hexane are chains, of which the molecules and intermolecular repulsion is large and not easy to gather. N-hexane is less viscous and polar than n-octane and cyclohexane, the dispersion effect of quantum dots in n-hexane solvent is better. Therefore, we used PbS quantum dots based on n-hexane for fiber preparation and experiment. We performed the silica fiber filled with the n-hexane solvent under a magnetic field ranging from 0 to 110 mT. As shown in Fig. 6(a), The sensitivities of n-hexane solvent and silica cladding fiber are, respectively, -3.1248×10−6 RIU/mT and 7.3798×10−7 RIU/mT. The magnetic field does not have obvious influence on n-hexane solvents. The three-dimensional refractive index distribution diagram of PbS QDs with a concentration of 8 mg/mL without applying an external magnetic field is shown in Fig. 6(b). The refractive index of the PbS QDs solution in the core part is much lower than that of silica in the cladding part.
The two-dimensional distribution of refractive index as a function of magnetic field for PbS QDs-doped liquid core fiber is shown in Fig. 7(a) and (b). Within the magnetic field range of 0-7.89 mT, the refractive index difference of quantum dot solution of fiber core decreases with the increase of the magnetic field.
Fig. 6. (a) The refractive index of n-hexane and silica cladding fiber with the magnetic field, (b) Three-dimensional refractive index distribution of PbS QDs.
Fig. 7. Distribution of refractive index as a function of magnetic fields in PbS QDs-doped liquid core fiber (a) sectional distribution, (b) fiber core part.
Next, the refractive index changes of 8 mg/mL PbS QDs at the radii of 4 nm, 5.25 nm, 5.75 nm, and 6.5 nm versus the magnetic field are shown in Fig. 8. Within the range of 0 to 7.89 mT, as the magnetic field increases, the refractive index of the quantum dots solution decreased by 1.316×10−2, 4.401×10−3, 2.594×10−3, and 4.800×10−4 RIU, respectively, which is compared with magnetic fluids [40]. The magnetic refractive effect of 4 nm-PbS QDs is strongest, which is consistent with the theoretical analysis, as shown in Eq. (2).
Without applying a magnetic field, the PbS QDs can be evenly separated in the solution. When the external magnetic field is applied, the structure of the quantum dots changes, and the spin unpaired electrons are introduced. In addition, the change of refractive index of quantum dots is closely related to magnetization and susceptibility. Due to the surface effect and spin coupling effect, as the size of the PbS QDs decreases, the HOMO-LUMO band gap decreases and the excitation becomes easier. As a result, the surface defect states increase. The spin magnetic moment is generated because the adjacent S atom lacks the paired electron, and interacts with it under the action of the magnetic field, so the magnetic system is enhanced and the magneto-refractive effect is more obvious. The results show that the refractive index of the PbS QDs decreases significantly with the increase of the magnetic field. Quantum dot radius have a great influence on the magneto-refractive effect of quantum dots, which should not be ignored.
Furthermore, we investigate the effect of concentration on magnetic refractive effect of PbS QDs-doped liquid core fiber, the refractive index difference of 4nm-PbS QDs with different concentrations as a function of the magnetic field were shown in Fig. 9. The refractive index changes of PbS QDs with c = 2 mg/mL, 4 mg/mL, 8 mg/mL and 12 mg/mL were -1.966×10−3, -4.554×10−3, -1.316×10−2, -6.344×10−3 RIU, respectively.
Fig. 9. 4 nm-PbS QDs refractive index change as a function of the magnetic field with different concentrations.
When the concentration is 12 mg/mL and the magnetic field increases greater than 2.25 mT, the refractive index of PbS QDs with the concentration of 12 mg/mL does not change obviously. However, when the concentration increases from 2 mg/mL to 8 mg/mL, the higher the concentration, the more obvious the refractive index change of PbS QDs with a magnetic field. This is mainly due to the fact that the n-hexane solution of quantum dots appears brown-black, the color will be darker when the higher the concentration. The magneto-refractive index of PbS QDs is saturated due to the influence of the absorbed light on the refractive index. Thus, the refractive index change is much smaller than when the concentration is 8 mg/mL, so it is very necessary to select an appropriate concentration.
4. Conclusion
The magnetic properties of PbS defects nanoclusters are studied based on the density functional theory. When defects exist in PbS nanoclusters, s and p states spin moment of Pb and S are coupled to generate spin magnetic moments, presenting unique magnetic properties, which are manifested as changes in the refractive index under the action of external magnetic fields. The magneto-refractive properties of PbS QDs with different concentrations and sizes were investigated under a magnetic field ranging from 0 to 7.89 mT. The experimental results show that the concentration and size of PbS QDs have an influence on the magneto-refractive sensitivity. The magnetic refractive index of PbS QDs is up to 1.316×10−2 RIU in the range of 0-7.89 mT, which can be used for magnetic field sensing applications.
Funding
National Key Research and Development Program of China (2020YFB1805800); Natural Science Foundation of Shanghai (22ZR1423000); National Natural Science Foundation of China (61735009, 61935002, 61975113, 62027818); 111 Project (D20031); Shanghai professional technical public service platform of advanced optical waveguide intelligent manufacturing and testing (19DZ2294000).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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